Intuitive robust stability metric for PID control of self-regulating processes

Area of Science:

• Control Systems Engineering
• Process Dynamics and Control
• Robust Control Theory

Background:

• Existing methods for analyzing closed-loop stability primarily focus on plant-model mismatch in process gain and dead time.
• These methods often overlook the significant impact of plant-model mismatch in the process time constant on system stability.

Purpose of the Study:

• To introduce a novel metric, the robust stability factor (RSF), for quantifying the effects of plant-model mismatch across gain, dead time, and time constant.
• To provide both an equation and a visual representation of the RSF using robustness plots derived from Bode and Nyquist criteria.
• To enhance the understanding of robust stability by illustrating its relationship with closed-loop performance under varying degrees of plant-model mismatch.

Main Methods:

• Development of the robust stability factor (RSF) metric.
• Application of Bode and Nyquist stability criteria to generate robustness plots.
• Theoretical analysis of the impact of dead time to time constant ratios on stability.
• Comparison of the robust stability of Internal Model Control (IMC)-PI tuning with other common tuning correlations (PI, PID, PID with Filter).

Main Results:

• The RSF metric effectively quantifies the influence of plant-model mismatch in gain, dead time, and time constant on closed-loop stability.
• Plant-model mismatch in the time constant can be as critical to stability as mismatch in gain or dead time.
• The impact of time constant mismatch is amplified for systems with small dead time to time constant ratios.
• Decreasing the closed-loop time constant in Internal Model Control (IMC) tuning broadens the range of dead time to time constant ratios for which time constant mismatch significantly affects stability.

Conclusions:

• The robust stability factor (RSF) offers a comprehensive approach to evaluating closed-loop stability robustness against plant-model mismatch.
• The findings highlight the critical, often underestimated, role of time constant mismatch in process control.
• The RSF provides valuable insights for controller tuning, particularly when comparing IMC-PI with other PID-based tuning strategies to ensure robust performance.